Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Orbifold adjunction formula and symplectic cobordisms between lens spaces

Weimin Chen

Geometry & Topology 8 (2004) 701–734

arXiv: math.GT/0403395

Abstract

Each lens space has a canonical contact structure which lifts to the distribution of complex lines on the three-sphere. In this paper, we show that a symplectic homology cobordism between two lens spaces, which is given with the canonical contact structure on the boundary, must be diffeomorphic to the product of a lens space with the unit interval. As one of the main ingredients in the proof, we also derive in this paper the adjunction and intersection formulae for pseudoholomorphic curves in an almost complex 4–orbifold, extending the relevant work of Gromov and McDuff in the manifold setting.

Keywords
cobordism of lens spaces, orbifold adjunction formula, symplectic 4–orbifolds, pseudoholomorphic curves
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57R80
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Publication
Received: 27 December 2003
Revised: 20 January 2004
Accepted: 3 May 2004
Published: 16 May 2004
Proposed: Yasha Eliashberg
Seconded: Robion Kirby, Ronald Fintushel
Authors
Weimin Chen
Mathematics Department
Tulane University
New Orleans
Louisiana 70118
USA